The retina of a human eye can detect light when radiant energy incident on it is at least 4.0x10^(-17)J. For light of 535nm (5.35x10^(-7) m) wavelength, how many PHOTONS does this energy correspond to?
E = hc/wavelength. Solve for energy of the 535 nm light. Then set up a proportion between what that is for 1 photon and the number of photons to reach the minimum energy.
To determine the number of photons corresponding to a given energy, we can use the formula:
Number of photons = Energy / Energy per photon
The energy per photon can be calculated using the formula:
Energy per photon = Planck's constant * speed of light / wavelength
First, let's calculate the energy per photon:
Planck's constant (h) = 6.62607015 × 10^(-34) J·s
Speed of light (c) = 2.998 × 10^8 m/s
Wavelength (λ) = 5.35 × 10^(-7) m
Energy per photon = (6.62607015 × 10^(-34) J·s * 2.998 × 10^8 m/s) / (5.35 × 10^(-7) m)
Energy per photon ≈ 3.72 × 10^(-19) J
Now we can calculate the number of photons:
Number of photons = (4.0 × 10^(-17) J) / (3.72 × 10^(-19) J/photon)
Number of photons ≈ 107.5 × 10^(0)
Number of photons ≈ 107.5
Therefore, the energy of 4.0 × 10^(-17) J corresponds to approximately 107.5 photons.